Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_pH 10 1.803423
beta2_pelagic 3 1.466120
beta2_yellow 2 1.447881
beta1_pelagic 7 1.429622
beta0_pelagic 6 1.388324
beta3_yellow 2 1.265938
beta1_yellow 5 1.260935
beta0_yellow 3 1.250179
beta4_pelagic 1 1.233184
parameter n badRhat_avg
beta3_pelagic 3 1.221127
beta3_pH 4 1.220794
beta0_pH 4 1.208879
beta2_pH 4 1.165727
tau_beta0_pH 2 1.133676
beta4_yellow 2 1.133350
beta3_black 1 1.120146
tau_beta0_pelagic 1 1.117169
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEO WKMA
beta0_pelagic 0 0 1 1 0 1 0 0 0 1 1 0 1 0
beta0_pH 0 0 0 0 1 1 0 0 0 0 1 0 0 1
beta0_yellow 0 0 0 0 0 0 0 0 1 0 1 0 0 1
beta1_pelagic 0 0 1 1 0 1 0 0 1 1 1 0 1 0
beta1_pH 1 1 0 0 1 1 0 0 0 1 1 1 0 1
beta1_yellow 1 0 1 0 0 1 0 0 0 0 1 0 0 1
beta2_pelagic 0 0 0 1 0 1 0 0 0 0 1 0 0 0
beta2_pH 0 0 1 0 0 1 1 0 0 0 1 0 0 0
beta2_yellow 0 0 1 0 0 0 0 0 0 0 1 0 0 0
beta3_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 1 0 0 0 0 1 0 1 0 0 0
beta3_pH 0 0 0 0 0 1 0 1 0 0 1 0 0 1
beta3_yellow 0 0 0 0 0 1 0 0 1 0 0 0 0 0
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0
beta4_yellow 0 1 0 0 0 0 0 0 0 0 0 1 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 1 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.118 0.074 -0.250 -0.122 0.039
mu_bc_H[2] -0.095 0.045 -0.171 -0.100 0.007
mu_bc_H[3] -0.438 0.070 -0.568 -0.439 -0.301
mu_bc_H[4] -0.999 0.196 -1.402 -0.997 -0.633
mu_bc_H[5] 0.878 0.883 -0.155 0.690 3.076
mu_bc_H[6] -2.143 0.324 -2.757 -2.151 -1.490
mu_bc_H[7] -0.461 0.111 -0.690 -0.460 -0.252
mu_bc_H[8] 0.251 0.353 -0.361 0.218 1.043
mu_bc_H[9] -0.287 0.136 -0.551 -0.287 -0.013
mu_bc_H[10] -0.110 0.069 -0.235 -0.111 0.036
mu_bc_H[11] -0.123 0.038 -0.197 -0.123 -0.046
mu_bc_H[12] -0.253 0.107 -0.484 -0.250 -0.054
mu_bc_H[13] -0.136 0.076 -0.281 -0.137 0.017
mu_bc_H[14] -0.303 0.097 -0.505 -0.300 -0.113
mu_bc_H[15] -0.342 0.050 -0.439 -0.343 -0.239
mu_bc_H[16] -0.243 0.385 -0.891 -0.274 0.586
mu_bc_R[1] 1.337 0.149 1.048 1.336 1.640
mu_bc_R[2] 1.444 0.094 1.257 1.445 1.624
mu_bc_R[3] 1.419 0.142 1.130 1.420 1.693
mu_bc_R[4] 0.893 0.198 0.487 0.899 1.254
mu_bc_R[5] 1.165 0.455 0.252 1.176 2.049
mu_bc_R[6] -1.618 0.398 -2.419 -1.616 -0.863
mu_bc_R[7] 0.304 0.186 -0.056 0.302 0.673
mu_bc_R[8] 0.522 0.195 0.125 0.523 0.904
mu_bc_R[9] 0.291 0.210 -0.144 0.305 0.657
mu_bc_R[10] 1.309 0.155 0.992 1.313 1.607
mu_bc_R[11] 1.035 0.098 0.837 1.035 1.228
mu_bc_R[12] 0.824 0.204 0.426 0.830 1.212
mu_bc_R[13] 1.025 0.104 0.817 1.027 1.220
mu_bc_R[14] 0.902 0.140 0.622 0.903 1.171
mu_bc_R[15] 0.781 0.112 0.561 0.782 1.002
mu_bc_R[16] 1.090 0.127 0.838 1.092 1.336
tau_pH[1] 5.171 0.430 4.375 5.154 6.036
tau_pH[2] 2.026 0.221 1.636 2.014 2.502
tau_pH[3] 2.301 0.237 1.880 2.289 2.792
beta0_pH[1,1] 0.565 0.170 0.219 0.573 0.887
beta0_pH[2,1] 1.346 0.198 0.916 1.359 1.701
beta0_pH[3,1] 1.401 0.176 1.026 1.411 1.724
beta0_pH[4,1] 1.575 0.213 1.108 1.587 1.954
beta0_pH[5,1] -0.878 0.303 -1.587 -0.851 -0.375
beta0_pH[6,1] -0.859 0.593 -2.641 -0.746 -0.078
beta0_pH[7,1] 0.273 0.733 -1.166 0.730 0.975
beta0_pH[8,1] -0.736 0.303 -1.423 -0.714 -0.227
beta0_pH[9,1] -0.697 0.280 -1.281 -0.686 -0.179
beta0_pH[10,1] 0.463 0.171 0.108 0.474 0.776
beta0_pH[11,1] -0.080 0.169 -0.432 -0.076 0.238
beta0_pH[12,1] 0.491 0.188 0.117 0.496 0.856
beta0_pH[13,1] 0.011 0.148 -0.282 0.010 0.303
beta0_pH[14,1] -0.320 0.164 -0.656 -0.313 -0.003
beta0_pH[15,1] -0.029 0.183 -0.402 -0.033 0.330
beta0_pH[16,1] -0.470 0.366 -1.385 -0.416 0.072
beta0_pH[1,2] 2.797 0.181 2.443 2.795 3.159
beta0_pH[2,2] 2.892 0.152 2.601 2.895 3.196
beta0_pH[3,2] 3.122 0.245 2.346 3.156 3.471
beta0_pH[4,2] 2.948 0.164 2.628 2.955 3.243
beta0_pH[5,2] 5.049 1.688 2.952 4.663 9.448
beta0_pH[6,2] 3.108 0.222 2.673 3.102 3.550
beta0_pH[7,2] 1.949 0.170 1.606 1.949 2.273
beta0_pH[8,2] 2.852 0.174 2.511 2.852 3.197
beta0_pH[9,2] 3.367 0.567 2.886 3.419 3.870
beta0_pH[10,2] 3.621 0.213 3.210 3.627 4.036
beta0_pH[11,2] -4.849 0.313 -5.481 -4.844 -4.246
beta0_pH[12,2] -4.786 0.390 -5.570 -4.774 -4.036
beta0_pH[13,2] -4.590 0.400 -5.366 -4.599 -3.792
beta0_pH[14,2] -5.576 0.464 -6.559 -5.556 -4.753
beta0_pH[15,2] -4.292 0.343 -4.970 -4.290 -3.620
beta0_pH[16,2] -4.852 0.384 -5.643 -4.833 -4.138
beta0_pH[1,3] 0.531 0.621 -0.897 0.624 1.375
beta0_pH[2,3] 1.988 0.442 0.765 2.117 2.468
beta0_pH[3,3] 2.087 0.408 1.284 2.118 2.707
beta0_pH[4,3] 2.735 0.503 1.207 2.878 3.222
beta0_pH[5,3] 1.728 2.080 -1.270 1.350 6.862
beta0_pH[6,3] -0.401 0.978 -2.146 -0.557 1.512
beta0_pH[7,3] -2.020 0.560 -3.162 -1.987 -1.000
beta0_pH[8,3] 0.286 0.189 -0.087 0.284 0.658
beta0_pH[9,3] -0.605 0.464 -2.036 -0.543 0.061
beta0_pH[10,3] -0.157 1.016 -2.325 0.059 1.286
beta0_pH[11,3] -0.165 0.323 -0.801 -0.171 0.498
beta0_pH[12,3] -0.873 0.347 -1.605 -0.852 -0.268
beta0_pH[13,3] -0.073 0.344 -0.707 -0.096 0.669
beta0_pH[14,3] -0.287 0.301 -0.820 -0.283 0.231
beta0_pH[15,3] -0.682 0.274 -1.248 -0.679 -0.158
beta0_pH[16,3] -0.389 0.287 -0.961 -0.384 0.154
beta1_pH[1,1] 3.002 0.309 2.439 2.989 3.651
beta1_pH[2,1] 2.203 0.331 1.694 2.165 3.027
beta1_pH[3,1] 2.019 0.272 1.542 2.005 2.595
beta1_pH[4,1] 2.365 0.308 1.844 2.338 3.055
beta1_pH[5,1] 2.318 0.415 1.681 2.260 3.351
beta1_pH[6,1] 4.324 1.308 2.457 4.072 7.414
beta1_pH[7,1] 2.818 1.660 0.168 2.698 7.052
beta1_pH[8,1] 4.292 1.059 2.737 4.106 6.786
beta1_pH[9,1] 2.378 0.395 1.725 2.327 3.342
beta1_pH[10,1] 2.068 0.227 1.659 2.064 2.534
beta1_pH[11,1] 3.264 0.213 2.871 3.255 3.716
beta1_pH[12,1] 2.545 0.218 2.118 2.542 2.974
beta1_pH[13,1] 2.963 0.218 2.556 2.957 3.414
beta1_pH[14,1] 3.424 0.216 3.004 3.423 3.845
beta1_pH[15,1] 2.531 0.231 2.089 2.531 2.984
beta1_pH[16,1] 4.115 0.643 3.196 4.026 5.708
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.008 0.066 0.000 0.000 0.043
beta1_pH[3,2] 0.073 0.281 0.000 0.000 1.228
beta1_pH[4,2] 0.027 0.151 0.000 0.000 0.419
beta1_pH[5,2] 0.038 0.414 0.000 0.000 0.033
beta1_pH[6,2] 0.053 0.388 0.000 0.000 0.814
beta1_pH[7,2] 0.013 0.154 0.000 0.000 0.050
beta1_pH[8,2] 0.010 0.101 0.000 0.000 0.065
beta1_pH[9,2] 0.391 4.638 0.000 0.000 1.250
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.685 0.343 6.003 6.680 7.372
beta1_pH[12,2] 6.463 0.471 5.595 6.444 7.475
beta1_pH[13,2] 6.985 0.444 6.152 6.980 7.871
beta1_pH[14,2] 7.210 0.486 6.324 7.186 8.221
beta1_pH[15,2] 6.765 0.370 6.044 6.763 7.505
beta1_pH[16,2] 7.444 0.428 6.630 7.426 8.315
beta1_pH[1,3] 3.070 1.337 1.466 2.706 6.583
beta1_pH[2,3] 5.149 14.931 0.001 0.932 39.586
beta1_pH[3,3] 2.069 7.351 0.001 0.878 12.277
beta1_pH[4,3] 41.229 56.810 0.002 1.997 153.606
beta1_pH[5,3] 3.167 2.277 0.072 2.781 8.628
beta1_pH[6,3] 2.245 1.078 0.036 2.311 4.088
beta1_pH[7,3] 2.864 0.566 1.833 2.836 4.074
beta1_pH[8,3] 2.744 0.341 2.085 2.734 3.437
beta1_pH[9,3] 2.654 0.484 1.850 2.613 3.878
beta1_pH[10,3] 3.606 1.135 1.921 3.424 6.009
beta1_pH[11,3] 2.757 0.386 2.001 2.754 3.533
beta1_pH[12,3] 4.140 0.436 3.361 4.121 5.066
beta1_pH[13,3] 1.655 0.365 0.865 1.666 2.330
beta1_pH[14,3] 2.551 0.376 1.889 2.549 3.231
beta1_pH[15,3] 1.977 0.296 1.384 1.977 2.572
beta1_pH[16,3] 1.798 0.321 1.187 1.793 2.433
beta2_pH[1,1] 0.490 0.123 0.303 0.475 0.789
beta2_pH[2,1] 0.526 0.205 0.209 0.499 1.009
beta2_pH[3,1] 0.583 0.270 0.241 0.534 1.223
beta2_pH[4,1] 0.480 0.168 0.227 0.458 0.880
beta2_pH[5,1] 1.632 1.223 0.202 1.472 4.689
beta2_pH[6,1] 0.162 0.059 0.074 0.152 0.309
beta2_pH[7,1] -0.903 1.448 -4.531 -0.652 0.921
beta2_pH[8,1] 0.221 0.081 0.119 0.205 0.416
beta2_pH[9,1] 0.420 0.204 0.166 0.383 0.904
beta2_pH[10,1] 0.603 0.188 0.342 0.573 1.080
beta2_pH[11,1] 0.790 0.211 0.475 0.762 1.277
beta2_pH[12,1] 1.358 0.498 0.734 1.249 2.580
beta2_pH[13,1] 0.744 0.229 0.412 0.707 1.301
beta2_pH[14,1] 0.837 0.217 0.526 0.802 1.368
beta2_pH[15,1] 0.808 0.311 0.417 0.750 1.503
beta2_pH[16,1] 0.378 0.171 0.170 0.328 0.820
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] -1.244 10.534 -21.449 -1.479 19.987
beta2_pH[3,2] -1.301 10.508 -21.897 -1.543 19.118
beta2_pH[4,2] -1.244 10.596 -22.307 -1.372 19.312
beta2_pH[5,2] 0.087 9.367 -18.381 0.015 19.970
beta2_pH[6,2] 0.184 9.441 -18.262 -0.005 20.267
beta2_pH[7,2] 0.032 9.161 -18.197 0.007 19.925
beta2_pH[8,2] 0.005 9.415 -18.797 -0.108 20.039
beta2_pH[9,2] 0.120 9.420 -18.403 0.030 20.262
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.539 4.492 -21.578 -8.447 -4.115
beta2_pH[12,2] -7.344 5.256 -20.997 -6.295 -0.858
beta2_pH[13,2] -7.120 5.188 -22.298 -5.695 -1.505
beta2_pH[14,2] -8.249 4.881 -21.181 -6.914 -2.484
beta2_pH[15,2] -9.173 4.518 -21.227 -8.042 -3.659
beta2_pH[16,2] -9.481 4.537 -21.733 -8.538 -3.923
beta2_pH[1,3] 1.277 2.115 0.113 0.418 6.697
beta2_pH[2,3] -0.883 3.867 -7.471 -0.823 7.621
beta2_pH[3,3] -2.151 3.724 -9.731 -1.970 5.980
beta2_pH[4,3] -1.091 3.953 -9.088 -1.264 8.148
beta2_pH[5,3] 9.965 6.073 1.010 8.989 23.685
beta2_pH[6,3] 9.906 6.058 0.659 9.035 23.360
beta2_pH[7,3] 9.472 5.983 0.876 8.675 22.576
beta2_pH[8,3] 10.663 5.533 2.573 9.822 23.295
beta2_pH[9,3] 9.624 6.183 0.433 8.853 23.511
beta2_pH[10,3] 1.639 2.334 0.288 0.682 8.245
beta2_pH[11,3] -2.031 1.489 -6.144 -1.614 -0.609
beta2_pH[12,3] -2.275 1.602 -6.964 -1.810 -0.934
beta2_pH[13,3] -2.250 2.219 -7.767 -1.907 2.190
beta2_pH[14,3] -2.485 1.577 -7.064 -2.049 -0.775
beta2_pH[15,3] -2.785 1.836 -8.228 -2.185 -0.967
beta2_pH[16,3] -2.767 1.940 -8.533 -2.152 -0.852
beta3_pH[1,1] 35.823 0.813 34.228 35.802 37.502
beta3_pH[2,1] 33.622 1.404 31.372 33.478 36.968
beta3_pH[3,1] 33.727 1.027 31.826 33.691 35.851
beta3_pH[4,1] 33.777 1.177 31.586 33.763 36.213
beta3_pH[5,1] 27.774 1.290 26.480 27.481 31.259
beta3_pH[6,1] 38.990 3.478 32.393 38.916 45.390
beta3_pH[7,1] 25.264 8.257 18.203 20.902 44.580
beta3_pH[8,1] 40.280 2.366 35.943 40.071 45.386
beta3_pH[9,1] 30.493 1.426 27.996 30.383 33.592
beta3_pH[10,1] 33.107 0.969 31.278 33.075 35.119
beta3_pH[11,1] 30.365 0.459 29.464 30.370 31.296
beta3_pH[12,1] 30.166 0.406 29.344 30.176 30.923
beta3_pH[13,1] 33.170 0.585 32.099 33.153 34.369
beta3_pH[14,1] 32.028 0.462 31.148 32.017 32.974
beta3_pH[15,1] 31.183 0.660 29.932 31.183 32.484
beta3_pH[16,1] 32.073 1.038 30.345 31.924 34.537
beta3_pH[1,2] 30.130 7.991 18.475 29.241 44.944
beta3_pH[2,2] 30.281 8.036 18.480 29.329 44.980
beta3_pH[3,2] 30.508 8.315 18.451 29.344 44.790
beta3_pH[4,2] 30.132 8.004 18.426 29.259 44.832
beta3_pH[5,2] 30.243 8.004 18.415 29.418 44.828
beta3_pH[6,2] 29.943 7.901 18.537 28.969 44.766
beta3_pH[7,2] 29.659 7.855 18.474 28.415 44.759
beta3_pH[8,2] 30.010 8.077 18.396 28.771 45.129
beta3_pH[9,2] 30.075 8.059 18.468 28.882 45.035
beta3_pH[10,2] 30.006 7.940 18.501 29.114 45.080
beta3_pH[11,2] 43.406 0.177 43.117 43.390 43.769
beta3_pH[12,2] 43.186 0.206 42.801 43.149 43.702
beta3_pH[13,2] 43.851 0.157 43.427 43.892 44.052
beta3_pH[14,2] 43.300 0.196 43.045 43.251 43.791
beta3_pH[15,2] 43.409 0.192 43.105 43.386 43.802
beta3_pH[16,2] 43.496 0.183 43.167 43.495 43.832
beta3_pH[1,3] 38.855 2.524 33.899 39.250 44.205
beta3_pH[2,3] 27.864 7.556 18.372 25.745 44.304
beta3_pH[3,3] 34.913 9.009 18.722 40.738 44.471
beta3_pH[4,3] 25.600 6.612 18.255 23.864 43.415
beta3_pH[5,3] 27.215 6.829 18.324 25.776 43.238
beta3_pH[6,3] 27.513 6.293 18.687 25.756 44.259
beta3_pH[7,3] 26.587 0.924 25.081 26.433 28.865
beta3_pH[8,3] 41.486 0.242 41.067 41.485 41.914
beta3_pH[9,3] 33.239 1.292 28.748 33.534 34.204
beta3_pH[10,3] 34.789 1.502 31.588 35.055 36.913
beta3_pH[11,3] 41.826 0.795 40.195 41.841 43.227
beta3_pH[12,3] 41.722 0.381 40.980 41.727 42.482
beta3_pH[13,3] 41.874 3.283 29.927 42.688 44.569
beta3_pH[14,3] 41.105 0.621 39.894 41.122 42.270
beta3_pH[15,3] 42.563 0.679 41.084 42.649 43.688
beta3_pH[16,3] 42.906 0.721 41.284 43.009 44.145
beta0_pelagic[1] 1.908 0.571 -0.058 2.096 2.423
beta0_pelagic[2] 1.083 0.742 -1.192 1.371 1.698
beta0_pelagic[3] 0.156 0.393 -0.959 0.215 0.725
beta0_pelagic[4] -0.026 0.711 -1.700 0.202 0.971
beta0_pelagic[5] 1.171 0.246 0.665 1.178 1.646
beta0_pelagic[6] 1.473 0.272 0.898 1.493 1.955
beta0_pelagic[7] 1.647 0.214 1.252 1.634 2.108
beta0_pelagic[8] 1.760 0.206 1.348 1.760 2.204
beta0_pelagic[9] 2.501 0.320 1.874 2.505 3.089
beta0_pelagic[10] 2.514 0.203 2.084 2.522 2.906
beta0_pelagic[11] 0.075 0.460 -0.928 0.128 0.751
beta0_pelagic[12] 1.685 0.140 1.422 1.686 1.961
beta0_pelagic[13] 0.337 0.172 -0.027 0.348 0.647
beta0_pelagic[14] -0.130 0.292 -0.781 -0.110 0.383
beta0_pelagic[15] -0.258 0.135 -0.518 -0.258 0.009
beta0_pelagic[16] 0.349 0.200 -0.140 0.382 0.664
beta1_pelagic[1] 0.355 0.587 0.000 0.090 2.390
beta1_pelagic[2] 0.477 0.737 0.000 0.141 2.709
beta1_pelagic[3] 0.962 0.639 0.227 0.828 3.168
beta1_pelagic[4] 1.217 0.737 0.010 0.985 2.929
beta1_pelagic[5] -0.080 0.312 -0.695 -0.073 0.532
beta1_pelagic[6] -0.107 0.463 -0.871 -0.171 0.747
beta1_pelagic[7] -0.025 0.308 -0.593 -0.026 0.586
beta1_pelagic[8] -0.006 0.282 -0.552 -0.011 0.564
beta1_pelagic[9] 0.193 0.499 -0.773 0.308 0.971
beta1_pelagic[10] 0.047 0.273 -0.476 0.043 0.602
beta1_pelagic[11] 3.748 1.144 2.169 3.624 6.045
beta1_pelagic[12] 2.789 0.292 2.236 2.788 3.390
beta1_pelagic[13] 2.799 0.648 1.762 2.710 4.311
beta1_pelagic[14] 4.440 1.189 2.833 4.185 7.239
beta1_pelagic[15] 2.895 0.242 2.398 2.902 3.343
beta1_pelagic[16] 3.379 0.603 2.674 3.237 5.067
beta2_pelagic[1] 1.706 2.989 -4.144 1.221 8.466
beta2_pelagic[2] 1.448 3.019 -3.199 0.953 8.551
beta2_pelagic[3] 2.051 2.413 0.061 1.111 8.347
beta2_pelagic[4] 2.426 2.431 0.210 1.589 8.526
beta2_pelagic[5] -0.006 0.668 -1.358 -0.006 1.410
beta2_pelagic[6] -0.131 0.700 -1.558 -0.159 1.281
beta2_pelagic[7] 0.004 0.686 -1.414 -0.009 1.439
beta2_pelagic[8] -0.008 0.651 -1.395 0.004 1.368
beta2_pelagic[9] 0.181 0.684 -1.294 0.258 1.487
beta2_pelagic[10] 0.019 0.660 -1.374 0.026 1.478
beta2_pelagic[11] 1.775 3.545 0.116 0.258 12.296
beta2_pelagic[12] 6.726 5.179 1.424 5.243 21.040
beta2_pelagic[13] 0.891 1.739 0.222 0.502 4.296
beta2_pelagic[14] 0.317 0.168 0.148 0.280 0.738
beta2_pelagic[15] 6.632 4.826 1.443 5.334 19.684
beta2_pelagic[16] 5.596 5.259 0.273 4.584 19.398
beta3_pelagic[1] 27.283 7.643 18.364 24.485 44.609
beta3_pelagic[2] 26.853 7.899 18.212 24.202 44.627
beta3_pelagic[3] 30.060 4.559 22.682 29.781 42.277
beta3_pelagic[4] 24.880 3.203 19.396 24.990 32.455
beta3_pelagic[5] 30.098 8.218 18.514 28.785 45.209
beta3_pelagic[6] 32.192 6.554 19.128 32.105 44.286
beta3_pelagic[7] 29.549 7.615 18.504 28.685 44.799
beta3_pelagic[8] 29.261 7.852 18.438 27.857 44.822
beta3_pelagic[9] 30.976 6.127 19.098 31.096 43.226
beta3_pelagic[10] 29.373 8.141 18.367 27.973 45.103
beta3_pelagic[11] 42.580 1.762 37.934 43.021 45.493
beta3_pelagic[12] 43.462 0.240 43.046 43.452 43.913
beta3_pelagic[13] 42.693 1.266 40.420 42.598 45.511
beta3_pelagic[14] 42.458 1.801 38.908 42.410 45.726
beta3_pelagic[15] 43.180 0.258 42.518 43.187 43.668
beta3_pelagic[16] 43.147 0.553 41.605 43.219 43.852
mu_beta0_pelagic[1] 0.726 0.977 -1.363 0.804 2.506
mu_beta0_pelagic[2] 1.808 0.389 1.042 1.823 2.535
mu_beta0_pelagic[3] 0.352 0.456 -0.534 0.352 1.292
tau_beta0_pelagic[1] 1.174 2.904 0.059 0.573 5.667
tau_beta0_pelagic[2] 2.755 2.874 0.247 1.986 10.099
tau_beta0_pelagic[3] 1.582 1.216 0.193 1.302 4.716
beta0_yellow[1] -0.524 0.190 -0.953 -0.511 -0.201
beta0_yellow[2] 0.486 0.160 0.152 0.496 0.770
beta0_yellow[3] -0.316 0.197 -0.747 -0.309 0.038
beta0_yellow[4] 0.693 0.423 -0.346 0.780 1.170
beta0_yellow[5] -1.259 0.398 -2.045 -1.256 -0.497
beta0_yellow[6] 0.278 0.212 -0.132 0.276 0.695
beta0_yellow[7] 0.989 0.371 -0.246 1.044 1.352
beta0_yellow[8] 0.791 0.544 -0.881 0.949 1.290
beta0_yellow[9] -0.178 0.337 -0.840 -0.158 0.363
beta0_yellow[10] 0.232 0.157 -0.069 0.233 0.543
beta0_yellow[11] -1.957 0.447 -2.812 -1.964 -1.113
beta0_yellow[12] -3.672 0.418 -4.535 -3.649 -2.929
beta0_yellow[13] -3.758 0.484 -4.824 -3.710 -2.928
beta0_yellow[14] -2.070 0.638 -3.109 -2.148 -0.256
beta0_yellow[15] -2.884 0.378 -3.673 -2.869 -2.145
beta0_yellow[16] -2.411 0.440 -3.273 -2.411 -1.514
beta1_yellow[1] 0.720 1.425 0.000 0.411 3.161
beta1_yellow[2] 1.149 0.473 0.603 1.062 2.529
beta1_yellow[3] 0.704 0.324 0.072 0.681 1.439
beta1_yellow[4] 1.799 1.131 0.695 1.389 5.034
beta1_yellow[5] 3.122 1.757 1.549 2.940 4.920
beta1_yellow[6] 2.279 0.351 1.586 2.272 2.946
beta1_yellow[7] 5.388 6.806 1.012 3.583 20.953
beta1_yellow[8] 2.471 6.267 0.033 1.953 7.589
beta1_yellow[9] 1.693 0.529 0.933 1.640 2.983
beta1_yellow[10] 2.409 0.446 1.606 2.381 3.332
beta1_yellow[11] 2.102 0.440 1.218 2.112 2.925
beta1_yellow[12] 2.475 0.430 1.697 2.439 3.405
beta1_yellow[13] 2.881 0.484 2.059 2.831 3.943
beta1_yellow[14] 2.215 0.526 1.067 2.234 3.198
beta1_yellow[15] 2.129 0.368 1.422 2.118 2.915
beta1_yellow[16] 2.164 0.440 1.283 2.160 3.031
beta2_yellow[1] -2.009 2.199 -7.410 -1.820 1.294
beta2_yellow[2] -1.983 1.738 -6.788 -1.715 -0.164
beta2_yellow[3] -2.211 2.102 -7.894 -1.642 -0.110
beta2_yellow[4] -1.270 1.764 -6.861 -0.445 -0.068
beta2_yellow[5] -4.544 2.918 -11.327 -4.054 -0.615
beta2_yellow[6] 3.636 2.231 0.961 3.075 9.065
beta2_yellow[7] -4.611 3.203 -11.714 -4.191 1.693
beta2_yellow[8] -2.573 3.991 -10.672 -2.417 6.054
beta2_yellow[9] 3.808 2.729 0.180 3.319 10.754
beta2_yellow[10] -4.668 2.764 -11.295 -4.222 -0.851
beta2_yellow[11] -4.172 2.216 -9.890 -3.731 -1.237
beta2_yellow[12] -4.492 2.241 -10.025 -4.056 -1.404
beta2_yellow[13] -4.261 2.064 -9.350 -3.832 -1.581
beta2_yellow[14] -4.260 2.456 -10.172 -3.877 -0.245
beta2_yellow[15] -4.108 2.234 -10.267 -3.607 -1.177
beta2_yellow[16] -4.425 2.131 -9.490 -4.059 -1.417
beta3_yellow[1] 26.672 7.396 18.310 23.656 43.813
beta3_yellow[2] 28.928 2.250 21.819 29.020 32.625
beta3_yellow[3] 32.781 3.415 23.674 32.873 39.597
beta3_yellow[4] 28.803 4.268 19.588 28.318 36.548
beta3_yellow[5] 33.363 1.332 30.888 33.411 35.350
beta3_yellow[6] 39.693 0.523 38.778 39.651 40.905
beta3_yellow[7] 20.355 2.245 18.442 20.042 27.012
beta3_yellow[8] 24.903 5.356 18.282 24.139 41.104
beta3_yellow[9] 37.703 2.044 35.599 37.573 42.960
beta3_yellow[10] 29.327 0.585 27.974 29.408 30.072
beta3_yellow[11] 45.285 0.533 43.991 45.383 45.969
beta3_yellow[12] 43.311 0.387 42.545 43.293 44.058
beta3_yellow[13] 44.845 0.378 44.015 44.917 45.466
beta3_yellow[14] 43.521 3.191 30.536 44.227 45.831
beta3_yellow[15] 45.187 0.507 44.200 45.177 45.966
beta3_yellow[16] 44.547 0.640 43.424 44.528 45.834
mu_beta0_yellow[1] 0.079 0.553 -1.103 0.078 1.175
mu_beta0_yellow[2] 0.124 0.484 -0.924 0.139 1.046
mu_beta0_yellow[3] -2.443 0.642 -3.451 -2.534 -0.830
tau_beta0_yellow[1] 2.084 2.560 0.097 1.259 8.878
tau_beta0_yellow[2] 1.241 1.228 0.145 0.937 4.083
tau_beta0_yellow[3] 1.507 3.073 0.091 0.888 6.365
beta0_black[1] -0.087 0.152 -0.385 -0.087 0.209
beta0_black[2] 1.916 0.125 1.679 1.919 2.170
beta0_black[3] 1.313 0.130 1.064 1.313 1.568
beta0_black[4] 2.424 0.130 2.174 2.426 2.670
beta0_black[5] 1.601 1.957 -2.840 1.707 5.500
beta0_black[6] 1.614 1.977 -2.974 1.694 5.282
beta0_black[7] 1.614 2.096 -3.108 1.676 5.849
beta0_black[8] 1.286 0.224 0.858 1.281 1.733
beta0_black[9] 2.441 0.250 1.970 2.439 2.934
beta0_black[10] 1.476 0.131 1.223 1.476 1.735
beta0_black[11] 3.486 0.148 3.196 3.484 3.777
beta0_black[12] 4.847 0.172 4.518 4.846 5.187
beta0_black[13] -0.120 0.235 -0.589 -0.114 0.326
beta0_black[14] 2.853 0.155 2.546 2.852 3.157
beta0_black[15] 1.293 0.150 0.996 1.291 1.597
beta0_black[16] 4.273 0.155 3.965 4.274 4.579
beta2_black[1] 3.558 2.325 0.754 2.954 9.396
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.079 1.750 -6.759 -1.488 -0.386
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.702 1.602 39.876 41.929 43.078
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.227 0.837 37.478 39.318 40.524
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.259 0.189 -0.629 -0.260 0.102
beta4_black[2] 0.235 0.181 -0.115 0.236 0.594
beta4_black[3] -0.929 0.188 -1.288 -0.930 -0.565
beta4_black[4] 0.414 0.210 0.020 0.413 0.811
beta4_black[5] 0.225 2.461 -4.350 0.175 5.201
beta4_black[6] 0.249 2.352 -4.118 0.198 5.047
beta4_black[7] 0.285 2.676 -4.396 0.156 4.931
beta4_black[8] -0.687 0.376 -1.445 -0.684 0.024
beta4_black[9] 1.440 1.003 -0.123 1.311 3.788
beta4_black[10] 0.021 0.184 -0.347 0.025 0.379
beta4_black[11] -0.699 0.208 -1.109 -0.694 -0.299
beta4_black[12] 0.172 0.314 -0.400 0.162 0.803
beta4_black[13] -1.190 0.221 -1.618 -1.192 -0.756
beta4_black[14] -0.184 0.229 -0.623 -0.182 0.264
beta4_black[15] -0.890 0.207 -1.288 -0.887 -0.489
beta4_black[16] -0.599 0.224 -1.047 -0.599 -0.164
mu_beta0_black[1] 1.294 0.917 -0.689 1.330 2.995
mu_beta0_black[2] 1.608 0.947 -0.752 1.669 3.393
mu_beta0_black[3] 2.523 0.956 0.437 2.551 4.418
tau_beta0_black[1] 0.632 0.594 0.056 0.442 2.227
tau_beta0_black[2] 1.911 3.595 0.055 0.847 10.086
tau_beta0_black[3] 0.241 0.156 0.053 0.202 0.641
beta0_dsr[11] -2.902 0.291 -3.486 -2.903 -2.338
beta0_dsr[12] 4.525 0.273 3.997 4.520 5.074
beta0_dsr[13] -1.354 0.333 -1.984 -1.336 -0.804
beta0_dsr[14] -3.670 0.515 -4.711 -3.667 -2.696
beta0_dsr[15] -1.929 0.274 -2.487 -1.928 -1.401
beta0_dsr[16] -2.984 0.364 -3.703 -2.974 -2.278
beta1_dsr[11] 4.839 0.302 4.246 4.841 5.413
beta1_dsr[12] 33.654 223.803 2.244 5.027 33.132
beta1_dsr[13] 2.873 0.400 2.297 2.838 3.539
beta1_dsr[14] 6.334 0.544 5.260 6.338 7.419
beta1_dsr[15] 3.325 0.278 2.788 3.320 3.902
beta1_dsr[16] 5.809 0.377 5.069 5.803 6.543
beta2_dsr[11] -8.284 2.366 -13.906 -7.920 -4.676
beta2_dsr[12] -7.094 2.664 -12.937 -6.913 -2.427
beta2_dsr[13] -6.253 2.630 -11.699 -6.274 -1.015
beta2_dsr[14] -6.102 2.653 -12.064 -5.919 -1.853
beta2_dsr[15] -7.794 2.452 -13.610 -7.416 -3.948
beta2_dsr[16] -7.917 2.372 -13.436 -7.566 -4.151
beta3_dsr[11] 43.492 0.146 43.226 43.492 43.775
beta3_dsr[12] 33.963 0.734 32.041 34.125 34.807
beta3_dsr[13] 43.239 0.334 42.808 43.187 43.862
beta3_dsr[14] 43.345 0.229 43.078 43.278 43.931
beta3_dsr[15] 43.502 0.182 43.169 43.501 43.846
beta3_dsr[16] 43.443 0.157 43.173 43.434 43.766
beta4_dsr[11] 0.583 0.215 0.163 0.581 1.009
beta4_dsr[12] 0.246 0.447 -0.624 0.238 1.160
beta4_dsr[13] -0.163 0.213 -0.585 -0.159 0.235
beta4_dsr[14] 0.148 0.240 -0.344 0.147 0.596
beta4_dsr[15] 0.725 0.214 0.319 0.721 1.146
beta4_dsr[16] 0.130 0.221 -0.310 0.131 0.553
beta0_slope[11] -1.940 0.161 -2.256 -1.938 -1.628
beta0_slope[12] -4.663 0.260 -5.184 -4.661 -4.161
beta0_slope[13] -1.381 0.272 -2.169 -1.339 -0.992
beta0_slope[14] -2.641 0.176 -2.976 -2.638 -2.295
beta0_slope[15] -1.365 0.160 -1.680 -1.364 -1.047
beta0_slope[16] -2.728 0.174 -3.079 -2.727 -2.385
beta1_slope[11] 4.598 0.293 4.040 4.594 5.164
beta1_slope[12] 5.012 0.520 4.020 4.987 6.055
beta1_slope[13] 3.013 0.678 2.245 2.862 5.242
beta1_slope[14] 6.539 0.553 5.477 6.526 7.659
beta1_slope[15] 3.042 0.280 2.498 3.041 3.616
beta1_slope[16] 5.369 0.386 4.622 5.370 6.118
beta2_slope[11] 7.949 2.231 4.427 7.633 12.978
beta2_slope[12] 7.031 2.440 2.890 6.756 12.618
beta2_slope[13] 5.316 3.078 0.273 5.514 11.287
beta2_slope[14] 6.450 2.484 2.365 6.221 12.075
beta2_slope[15] 7.446 2.338 3.758 7.116 12.686
beta2_slope[16] 7.584 2.322 3.943 7.218 12.875
beta3_slope[11] 43.477 0.150 43.206 43.472 43.765
beta3_slope[12] 43.410 0.222 43.069 43.384 43.857
beta3_slope[13] 43.608 0.535 42.679 43.665 44.647
beta3_slope[14] 43.323 0.172 43.099 43.285 43.768
beta3_slope[15] 43.512 0.197 43.157 43.512 43.874
beta3_slope[16] 43.453 0.170 43.165 43.438 43.793
beta4_slope[11] -0.573 0.216 -1.000 -0.576 -0.163
beta4_slope[12] -1.391 0.657 -2.854 -1.322 -0.312
beta4_slope[13] 0.057 0.219 -0.363 0.054 0.494
beta4_slope[14] -0.181 0.260 -0.659 -0.185 0.344
beta4_slope[15] -0.727 0.210 -1.137 -0.728 -0.326
beta4_slope[16] -0.195 0.231 -0.637 -0.201 0.253
sigma_H[1] 0.207 0.056 0.106 0.204 0.330
sigma_H[2] 0.172 0.030 0.118 0.170 0.235
sigma_H[3] 0.196 0.043 0.118 0.193 0.288
sigma_H[4] 0.417 0.076 0.294 0.408 0.585
sigma_H[5] 1.003 0.208 0.629 0.995 1.430
sigma_H[6] 0.424 0.202 0.048 0.419 0.850
sigma_H[7] 0.300 0.060 0.208 0.292 0.447
sigma_H[8] 0.415 0.085 0.281 0.407 0.602
sigma_H[9] 0.525 0.127 0.322 0.510 0.813
sigma_H[10] 0.208 0.043 0.131 0.204 0.303
sigma_H[11] 0.278 0.046 0.201 0.274 0.379
sigma_H[12] 0.436 0.165 0.206 0.412 0.772
sigma_H[13] 0.215 0.038 0.147 0.212 0.299
sigma_H[14] 0.509 0.094 0.347 0.504 0.713
sigma_H[15] 0.246 0.041 0.178 0.241 0.335
sigma_H[16] 0.225 0.044 0.154 0.220 0.327
lambda_H[1] 3.062 3.907 0.145 1.782 13.893
lambda_H[2] 8.212 7.465 0.823 6.134 28.014
lambda_H[3] 6.035 9.203 0.273 3.033 30.518
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 5.355 15.695 0.037 1.129 47.302
lambda_H[6] 7.597 14.536 0.009 1.359 48.440
lambda_H[7] 0.014 0.010 0.002 0.012 0.040
lambda_H[8] 8.518 10.842 0.154 4.890 37.932
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.312 1.190 0.032 0.194 1.049
lambda_H[11] 0.251 0.361 0.011 0.127 1.237
lambda_H[12] 4.690 6.075 0.181 2.758 21.262
lambda_H[13] 3.458 3.240 0.236 2.557 11.631
lambda_H[14] 3.445 4.566 0.216 2.036 14.996
lambda_H[15] 0.024 0.033 0.003 0.016 0.089
lambda_H[16] 0.807 1.212 0.039 0.402 3.876
mu_lambda_H[1] 4.344 1.919 1.197 4.182 8.609
mu_lambda_H[2] 3.908 1.935 0.688 3.819 7.872
mu_lambda_H[3] 3.537 1.903 0.711 3.226 7.739
sigma_lambda_H[1] 8.594 4.304 2.015 7.893 18.164
sigma_lambda_H[2] 8.522 4.635 1.163 8.139 18.277
sigma_lambda_H[3] 6.434 4.147 0.962 5.536 16.632
beta_H[1,1] 6.896 1.106 4.163 7.080 8.534
beta_H[2,1] 9.877 0.486 8.795 9.916 10.795
beta_H[3,1] 7.994 0.785 6.178 8.098 9.255
beta_H[4,1] 9.384 8.003 -6.947 9.606 24.806
beta_H[5,1] 0.180 2.292 -4.848 0.447 4.035
beta_H[6,1] 3.242 3.951 -6.882 4.633 7.673
beta_H[7,1] 0.922 5.793 -11.866 1.398 10.964
beta_H[8,1] 1.217 2.844 -2.367 1.229 3.360
beta_H[9,1] 12.986 5.696 1.411 13.054 23.735
beta_H[10,1] 7.076 1.734 3.278 7.177 10.291
beta_H[11,1] 4.956 3.602 -3.340 5.749 9.932
beta_H[12,1] 2.600 1.034 0.789 2.551 5.000
beta_H[13,1] 9.030 0.948 7.018 9.125 10.523
beta_H[14,1] 2.200 1.037 0.116 2.192 4.329
beta_H[15,1] -6.197 3.739 -13.165 -6.341 1.917
beta_H[16,1] 3.602 2.804 -0.826 3.205 10.725
beta_H[1,2] 7.908 0.244 7.425 7.910 8.364
beta_H[2,2] 10.027 0.136 9.757 10.027 10.295
beta_H[3,2] 8.953 0.200 8.562 8.951 9.348
beta_H[4,2] 3.553 1.526 0.560 3.541 6.642
beta_H[5,2] 2.010 0.942 0.134 2.021 3.777
beta_H[6,2] 5.751 1.030 3.318 5.918 7.343
beta_H[7,2] 2.468 1.115 0.528 2.403 4.829
beta_H[8,2] 3.040 0.891 1.499 3.142 4.236
beta_H[9,2] 3.518 1.103 1.432 3.486 5.717
beta_H[10,2] 8.201 0.344 7.472 8.216 8.842
beta_H[11,2] 9.789 0.644 8.852 9.668 11.263
beta_H[12,2] 3.939 0.369 3.280 3.923 4.700
beta_H[13,2] 9.120 0.258 8.650 9.111 9.654
beta_H[14,2] 4.024 0.358 3.325 4.016 4.747
beta_H[15,2] 11.373 0.681 9.923 11.409 12.587
beta_H[16,2] 4.542 0.824 2.986 4.546 6.221
beta_H[1,3] 8.445 0.240 8.002 8.436 8.935
beta_H[2,3] 10.069 0.116 9.845 10.066 10.301
beta_H[3,3] 9.629 0.164 9.314 9.621 9.974
beta_H[4,3] -2.489 0.891 -4.334 -2.486 -0.770
beta_H[5,3] 3.845 0.595 2.625 3.863 4.974
beta_H[6,3] 7.878 1.166 6.325 7.498 10.478
beta_H[7,3] -2.550 0.762 -4.098 -2.537 -1.076
beta_H[8,3] 5.214 0.438 4.657 5.171 6.051
beta_H[9,3] -2.889 0.735 -4.371 -2.859 -1.471
beta_H[10,3] 8.703 0.273 8.179 8.702 9.240
beta_H[11,3] 8.535 0.295 7.873 8.565 9.049
beta_H[12,3] 5.253 0.312 4.545 5.293 5.758
beta_H[13,3] 8.836 0.179 8.468 8.838 9.187
beta_H[14,3] 5.725 0.274 5.127 5.743 6.209
beta_H[15,3] 10.362 0.316 9.764 10.357 11.007
beta_H[16,3] 6.214 0.613 4.879 6.280 7.223
beta_H[1,4] 8.244 0.181 7.858 8.257 8.562
beta_H[2,4] 10.126 0.122 9.862 10.131 10.339
beta_H[3,4] 10.121 0.165 9.767 10.136 10.415
beta_H[4,4] 11.801 0.457 10.915 11.796 12.694
beta_H[5,4] 5.479 0.732 4.317 5.389 7.196
beta_H[6,4] 7.046 0.913 5.021 7.341 8.268
beta_H[7,4] 8.173 0.358 7.472 8.166 8.877
beta_H[8,4] 6.709 0.231 6.279 6.719 7.125
beta_H[9,4] 7.213 0.459 6.303 7.216 8.132
beta_H[10,4] 7.736 0.234 7.297 7.728 8.218
beta_H[11,4] 9.382 0.201 8.976 9.387 9.759
beta_H[12,4] 7.137 0.207 6.732 7.136 7.573
beta_H[13,4] 9.047 0.142 8.770 9.049 9.328
beta_H[14,4] 7.738 0.216 7.323 7.734 8.159
beta_H[15,4] 9.472 0.235 9.008 9.472 9.932
beta_H[16,4] 9.353 0.243 8.917 9.343 9.857
beta_H[1,5] 8.974 0.148 8.677 8.978 9.260
beta_H[2,5] 10.783 0.092 10.604 10.783 10.962
beta_H[3,5] 10.930 0.173 10.621 10.920 11.299
beta_H[4,5] 8.378 0.465 7.487 8.366 9.339
beta_H[5,5] 5.441 0.571 4.125 5.479 6.465
beta_H[6,5] 8.792 0.628 7.894 8.639 10.241
beta_H[7,5] 6.816 0.332 6.163 6.808 7.476
beta_H[8,5] 8.212 0.203 7.865 8.201 8.619
beta_H[9,5] 8.190 0.475 7.207 8.193 9.137
beta_H[10,5] 10.103 0.220 9.674 10.098 10.547
beta_H[11,5] 11.515 0.228 11.059 11.513 11.971
beta_H[12,5] 8.485 0.198 8.081 8.479 8.886
beta_H[13,5] 10.012 0.131 9.766 10.015 10.263
beta_H[14,5] 9.203 0.234 8.771 9.194 9.686
beta_H[15,5] 11.171 0.235 10.702 11.172 11.612
beta_H[16,5] 9.919 0.180 9.550 9.925 10.261
beta_H[1,6] 10.193 0.191 9.859 10.178 10.618
beta_H[2,6] 11.512 0.108 11.299 11.510 11.729
beta_H[3,6] 10.807 0.162 10.460 10.816 11.105
beta_H[4,6] 12.884 0.824 11.199 12.913 14.491
beta_H[5,6] 5.906 0.591 4.756 5.886 7.105
beta_H[6,6] 8.819 0.666 7.037 8.949 9.760
beta_H[7,6] 9.776 0.555 8.680 9.767 10.844
beta_H[8,6] 9.527 0.260 9.048 9.538 9.973
beta_H[9,6] 8.482 0.797 6.964 8.479 10.160
beta_H[10,6] 9.531 0.314 8.852 9.558 10.076
beta_H[11,6] 10.810 0.352 10.056 10.835 11.429
beta_H[12,6] 9.370 0.260 8.868 9.362 9.902
beta_H[13,6] 11.052 0.164 10.761 11.044 11.401
beta_H[14,6] 9.826 0.291 9.244 9.824 10.394
beta_H[15,6] 10.831 0.421 9.991 10.832 11.660
beta_H[16,6] 10.537 0.247 10.000 10.554 11.005
beta_H[1,7] 10.908 0.897 8.626 11.015 12.400
beta_H[2,7] 12.218 0.432 11.360 12.223 13.089
beta_H[3,7] 10.530 0.651 9.127 10.587 11.652
beta_H[4,7] 2.500 4.211 -5.514 2.495 11.066
beta_H[5,7] 6.472 1.784 3.298 6.406 10.314
beta_H[6,7] 9.670 2.439 4.794 9.616 15.649
beta_H[7,7] 10.850 2.784 5.464 10.738 16.671
beta_H[8,7] 10.954 0.930 9.460 10.910 12.650
beta_H[9,7] 4.334 4.154 -4.038 4.411 12.447
beta_H[10,7] 9.823 1.450 7.207 9.727 12.938
beta_H[11,7] 10.982 1.705 7.757 10.884 14.656
beta_H[12,7] 9.979 0.955 7.922 10.062 11.570
beta_H[13,7] 11.645 0.759 9.829 11.748 12.834
beta_H[14,7] 10.389 0.972 8.323 10.445 12.045
beta_H[15,7] 12.026 2.223 7.750 11.985 16.509
beta_H[16,7] 12.308 1.327 10.168 12.112 15.452
beta0_H[1] 8.839 14.435 -17.012 8.897 35.323
beta0_H[2] 10.662 6.005 -1.535 10.626 22.845
beta0_H[3] 9.787 10.035 -10.196 9.869 29.854
beta0_H[4] 3.845 181.018 -367.530 3.701 367.756
beta0_H[5] 4.672 22.885 -39.823 4.560 51.847
beta0_H[6] 7.897 48.796 -100.567 7.893 113.104
beta0_H[7] 6.439 129.464 -263.759 4.949 264.048
beta0_H[8] 6.481 21.883 -13.986 6.485 26.738
beta0_H[9] 5.778 120.973 -238.596 5.516 242.270
beta0_H[10] 7.399 32.208 -59.605 7.619 71.473
beta0_H[11] 10.789 49.124 -92.019 10.824 111.644
beta0_H[12] 6.589 12.151 -15.153 6.692 29.272
beta0_H[13] 9.718 11.436 -11.898 9.735 30.888
beta0_H[14] 7.273 11.459 -15.736 7.085 32.611
beta0_H[15] 5.284 107.566 -217.736 5.969 220.853
beta0_H[16] 8.776 27.346 -45.174 8.242 68.610